The ergodicity of weak Hilbert spaces
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Erratum: Proc. Amer. Math. Soc. 148 (2020), 3199-3201.
Abstract:
This paper complements a recent result of Dilworth, Ferenczi, Kutzarova and Odell regarding the ergodicity of strongly asymptotic $\ell _p$ spaces. We state this result in a more general form, involving domination relations, and we show that every asymptotically Hilbertian space which is not isomorphic to $\ell _2$ is ergodic. In particular, every weak Hilbert space which is not isomorphic to $\ell _2$ must be ergodic. Throughout the paper we construct explicitly the maps which establish the fact that the relation $E_0$ is Borel reducible to isomorphism between subspaces of the Banach spaces involved.References
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Additional Information
- Razvan Anisca
- Affiliation: Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, P7B 5E1, Canada
- MR Author ID: 621000
- Email: ranisca@lakeheadu.ca
- Received by editor(s): May 29, 2009
- Received by editor(s) in revised form: August 5, 2009
- Published electronically: October 30, 2009
- Additional Notes: The author was supported in part by NSERC Grant 312594-05
- Communicated by: Nigel J. Kalton
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1405-1413
- MSC (2010): Primary 46B20; Secondary 46B15
- DOI: https://doi.org/10.1090/S0002-9939-09-10164-8
- MathSciNet review: 2578532